Atlas › Modular forms › Weight 4 › Level 59 › 59.4.a

Newspace 59.4.a: $S_{4}^{\mathrm{new}}(\Gamma_0(59))$

Newforms

Label	Dim	Coefficient field	Trace form	AL signs	Sign
59.4.a.a	2	$\mathbb{Q}(\sqrt{5})$	$2q - 4q^{2} - 2q^{3} + 2q^{4} + 6q^{5} + 4q^{6} - 22q^{7} + O(q^{8})$	−	$-1$
59.4.a.b	2	$\mathbb{Q}(\sqrt{17})$	$2q + q^{2} - q^{3} - 7q^{4} - 31q^{5} - 26q^{6} - 8q^{7} + O(q^{8})$	−	$-1$
59.4.a.c	10	degree 10	$10q + 3q^{2} + 3q^{3} + 55q^{4} + 15q^{5} + 26q^{6} + 40q^{7} + O(q^{8})$	+	$+1$

Hecke characteristic polynomials

The eigenvalue of $T = T_{2} + T_{3}$ generates each orbit's coefficient field; on the newspace its characteristic polynomial factors over $\mathbb{Q}$ as one irreducible factor per orbit:

Orbit	Characteristic polynomial of $T$
59.4.a.a	$x^{2} + 6x + 4$
59.4.a.b	$x^{2} - 17$
59.4.a.c	$x^{10} - 6x^{9} - 277x^{8} + 2120x^{7} + 19917x^{6} - 208716x^{5} - 56866x^{4} + 4919894x^{3} - 11511581x^{2} - 2961280x + 8601826$

Dimensions

Newforms $S_{4}^{\mathrm{new}}(\Gamma_0(59))$	14
Old forms	0
Cusp forms $S_{4}(\Gamma_0(59))$	14
Eisenstein series $E_{4}(\Gamma_0(59))$	2
Modular forms $M_{4}(\Gamma_0(59))$	16

Decomposition of the old subspace

The old subspace is 0.

Provenance

Stored in the atlas: computed by Sagebrush's modular symbols engine in 0.096 s (one thread) and proven: the dimensions are certified, and the characteristic polynomial of $T$ over $\mathbb{Z}$ is reconstructed by CRT past a rigorous coefficient bound.

The engine's checks

dim M^+ at levels [1, 59]: [1, 16] (certified at ell = 2147482481)
T = [(2, 1), (3, 1)]; h of degree 14 = 1 x 14 (phi(ord eps) x dim S_k^new); 2 primes, 0 rejected

Open in the notebook · JSON · stored data

Recompute it yourself

In Sage mode at sagebrush.space (or npx sagebrush --sage):

newform_orbits(59, 4)

With the Rust engine (source), in engine/:

cargo run --release -p sagebrush-web --example atlas -- 59:4 1000

← 58.4.a · 60.4.a →